Pick the relation: C = C₀·e−kt, LD = Vd·C/(S·F), maintenance rate = CL·Css/(S·F), τ = ln(Cpeak/Ctrough)/k.
For kidney function, estimate CrCl with Cockcroft–Gault first, then scale the dose or the interval.
Check the result: levels fall by half every half-life, and steady state takes about five half-lives.
Pharmacy calculations
Percentage strength
% w/v = g per 100 mL
Amount in a solution
g = % × mL / 100
Ratio strength
1:X = 1 g in X mL; % = 100 / X
Reconstitution
final volume = diluent + powder volume
Concentration
mg/mL = drug in vial / final volume
Alligation
parts of H = T − L, parts of L = H − T
Water or base
0%
Pediatric & critical-care dosing
Daily dose
mg/day = mg/kg/day × weight (kg)
Doses per day
number = 24 h / dosing interval (h)
Pounds to kilograms
kg = lb / 2.2
Infusion concentration
units/mL = units in bag / bag volume
Pump rate
mL/h = dose per hour / concentration
Titrated drip
mL/h = mcg/kg/min × kg × 60 / (mcg/mL)
Dose from pump rate
mcg/kg/min = mL/h × (mcg/mL) / (60 × kg)
Units
1 mg = 1000 mcg
2Practice problems
1.Clinical pharmacokineticsMedium
Practice exercise (made-up values, not clinical guidance). A patient has a lidocaine clearance of 750 mL/min. What infusion rate R in mg/min keeps the steady-state level at 2 mg/L?
CL = 750 mL/minCss = 2 mg/L
R = mg/min
2.Clinical pharmacokineticsHard
Practice exercise (made-up values, not clinical guidance). A 50 kg patient takes oral aminophylline (S = 0.8, F = 1) every 12 h. The theophylline clearance is 0.045 L/kg/h. Each dose is 450 mg of aminophylline. Find the average steady-state level Css,avg.
A solution has a ratio strength of 1:1000. You need 0.84 mg. Draw up the volume in the 1 mL syringe: what volume V is that?
1:10000.84 mg
V = mL
4.Pharmacy calculationsHard
A vial holds 1000 mg of powder. You add 4.6 mL of diluent, and the powder adds 0.4 mL of volume. The prescription is 300 mg. Draw up the dose: what volume V do you give?
1000 mg4.6 mL + 0.4 mL300 mg
V = mL
5.Pediatric & critical-care dosingMedium
Practice exercise (made-up values, not clinical guidance). A practice protocol calls for a heparin bolus of 80 units/kg for a patient who weighs 64 kg. The vial contains 1 000 units/mL. What volume V do you draw up? Round to one decimal place.
80 units/kg64 kg1 000 units/mL
V = mL
6.Pediatric & critical-care dosingHard
Practice exercise (made-up values, not clinical guidance). A bag contains dopamine 400 mg in 250 mL. The order is 8 mcg/kg/min for a patient who weighs 97 kg. At what rate R do you set the pump, in mL/h? Round to one decimal place.
400 mg/250 mL8 mcg/kg/min97 kg
R = mL/h
7.PharmacologyMedium
When does oseltamivir give the most benefit in influenza?
AWhen started within 48 hours of the first symptoms
BOnly after a bacterial pneumonia has developed
CAt any time, as the timing makes no difference
DOnly after symptoms have lasted at least one week
8.PharmacologyHard
A patient with myasthenia gravis took extra pyridostigmine doses. She now has increasing weakness, heavy salivation, sweating, small pupils and diarrhoea. What is the most likely cause?
AA stroke unrelated to the medication
BMyasthenic crisis from too little anticholinesterase drug
CCholinergic crisis from too much anticholinesterase drug
DAn allergic reaction to pyridostigmine
3Solutions
1.Clinical pharmacokinetics
Answer: R = 1.5 mg/min
Clearance and volume: at steady state the dosing rate equals the elimination rate, so the maintenance rate = CL × Css. A loading dose is LD = Vd × C/(S × F), with S the salt factor (fraction of active drug in the salt) and F the bioavailability (1 for IV). From two levels, k = ln(C₁/C₂)/Δt; for an IV bolus Vd = dose/C₀ and CL = k × Vd. The numbers are for practice only; at the bedside always follow local protocols and have high-risk doses double-checked.
Clearance in L/min
750 mL/min = 0.75 L/min
Infusion rate
R = 0.75·2 = 1.5 mg/min
Answer
R = 1.5 mg/min
2.Clinical pharmacokinetics
Answer: Css,avg = 13.33 mg/L
Designing a regimen: with rapid IV doses the level falls from peak to trough during the interval, so τ = ln(Cpeak/Ctrough)/k and the dose that restores the peak is Vd × (Cpeak − Ctrough). The average steady-state level is Css,avg = S·F·dose/(CL·τ). An infusion rises as C = (R/CL)(1 − e−kt). For a drug cleared by the kidneys, the dose is scaled with the creatinine clearance. The numbers are for practice only; at the bedside always follow local protocols and have high-risk doses double-checked.
Strength to volume: turn the strength into mg per mL first. A w/v percentage is grams per 100 mL, so x% = 10x mg/mL. A ratio strength 1:n is 1 g in n mL. After reconstitution the concentration is the powder's dose over the final volume (diluent + powder volume). Then volume = dose/concentration.
Strength in mg/mL
1000 mg/1000 mL = 1 mg/mL
Volume
V = 0.84/1 = 0.84 mL
Answer
V = 0.84 mL
4.Pharmacy calculations
Answer: V = 1.5 mL
Strength to volume: turn the strength into mg per mL first. A w/v percentage is grams per 100 mL, so x% = 10x mg/mL. A ratio strength 1:n is 1 g in n mL. After reconstitution the concentration is the powder's dose over the final volume (diluent + powder volume). Then volume = dose/concentration.
Final volume and concentration
4.6 + 0.4 = 5 mL
C = 1000/5 = 200 mg/mL
Volume
V = 300/200 = 1.5 mL
Answer
V = 1.5 mL
5.Pediatric & critical-care dosing
Answer: V = 5.1 mL
Heparin and insulin infusions: concentration = units in the bag/bag volume (units/mL). Pump rate (mL/h) = units per hour/concentration, and units per hour = mL/h × concentration. For a weight-based order, units/h = units/kg/h × weight first. A bolus volume = units needed/vial strength. The numbers are for practice only; at the bedside always follow local protocols and have high-risk doses double-checked.
Units needed
80·64 = 5 120 units
Volume
V = 5120/1000 = 5.12 ≈ 5.1 mL
Answer
V = 5.1 mL
6.Pediatric & critical-care dosing
Answer: R = 29.1 mL/h
Titrated drips: first find the concentration in mcg/mL (mg × 1000/mL). For a weight-based order, mcg/min = mcg/kg/min × weight. Then mL/h = mcg/min × 60/concentration. Working backwards, mcg/kg/min = mL/h × concentration/(60 × weight). The numbers are for practice only; at the bedside always follow local protocols and have high-risk doses double-checked.
Concentration
400 mg = 400 000 mcg
400 000/250 = 1600 mcg/mL
Dose per minute and per hour
8·97 = 776 mcg/min
776·60 = 46560 mcg/h
Pump rate
R = 46560/1600 = 29.1 mL/h
Answer
R = 29.1 mL/h
7.Pharmacology
Answer: A · When started within 48 hours of the first symptoms
Why this is the answer
Neuraminidase inhibitors work best early, while the virus is multiplying. Started within 48 hours, they shorten illness; in high-risk or hospitalised patients they may still be given later.
Answer
A · When started within 48 hours of the first symptoms
8.Pharmacology
Answer: C · Cholinergic crisis from too much anticholinesterase drug
Why this is the answer
Excess acetylcholine causes muscarinic signs (salivation, sweating, miosis, diarrhoea) and depolarising weakness. In myasthenic crisis, weakness occurs without these cholinergic signs; both can cause respiratory failure.
Answer
C · Cholinergic crisis from too much anticholinesterase drug